Question

Radius of a cylinder is $r$ and height is $h$. find the change in the volume if its height is doubled.

Answer 1

Given that,

The radius and height of a cylinder is $r$ and $h$ respectively.

To find out,

The change in volume, if its height is doubled.

We know that, volume of a cylinder is $\pi r^{2}h$.

Initially, radius $=r$ and height $=h$.

Hence, $V=\pi r^{2}h$

After the height is doubled, radius $=r$ and height $=2h$.

Hence, $V_{new}=\pi r^2\left(2h\right)$

$=2{\pi r}^{2}h$

Now, change in volume $\left(\Delta V\right)=2{\pi r}^{2}h-\pi r^{2}h$

$=\pi r^{2}h$

Here, $\frac{\Delta V}{V}=1$

$\therefore$ Change in volume $=100\%$

That is, the volume is doubled.

Hence, when the height of the cylinder is doubled, its volume is doubled or it increases by $100\%$.